Association rule mining is one of the most important fields in data mining and knowledge discovery in databases. Rules explosion is a problem of concern, as conventional mining algorithms often produce too many rules for decision makers to digest. Instead, this paper concentrates on a smaller set of rules, namely, a set of simple association rules each with its consequent containing only a single attribute. Such a rule set can be used to derive all other association rules, meaning that the original rule set based on conventional algorithms can be 'recovered' from the simple rules without any information loss. The number of simple rules is much less than the number of all rules. Moreover, corresponding algorithms are developed such that certain forms of rules (e.g. 'P double right arrow ?' or '? double right arrow Q') can be generated in a more efficient manner based on simple rules. (C) 2002 Elsevier Science Ltd. All rights reserved.